% GAUTIER LE BIHAN - 2020
% Replication files for “Shocks vs Menu Costs: Patterns of Price Rigidity in an Estimated Multi-Sector Menu-Cost Model�? –Review of Economics and Statistics
% Multisector general equilibrium CalvoPlus model
%% Based on codes by   Nakamura and Steinsson, 
%**************************************************************
function [f2, avfracup2,    med2,    interq2, kur2]=geNCalvoPlus_SMM(p0, mu_c, sig_eps_a, rho_a,weight_j );
    
 

% Set Fixed Parameters
%**************************************************************

theta = 4;    % Elasticity of demand
psi = 0;     % One over the Frisch elasticity of labor supply
gamma = 1;   % coefficient of relative risk aversion
FlexSSL = 1/3; % Steady State labor under flexible prices
beta = 0.96^(1/12);   % Discount factor

% Parameters of the process followed by nominal aggregate demand
% log(S_t) - log(S_t-1) = mu + nu_t
% where nu_t ~ N(0,sigma_eta^2), i.i.d.
mu = 0.0028;   %% Inflation trend
sigma_eta = 0.0065; 


mu = 0.00125;   %% Inflation trend
sigma_eta = 0.0028; 


% Set sector specific parameters
%***************************************************************
% NB: Edges of the rad grid need to be extra padded in the multi-sector 
% model because the sectors have different mean rad.
param_agg=[tanh(0.0552582422061334); 0.0345297530098889; exp(-3.22066898186641); tanh(0.850810309615751)];
NSectors = 2;
sm = 0.0;
sigma_eps     = [ param_agg(3) sig_eps_a]';
alphaCalvo    = [1-param_agg(1)  1-p0 ]';
  % pa           = [p_a    p_a ]';
    rho           = [param_agg(4)    rho_a ]';
SectorWeights = [ 0.57-weight_j    weight_j]';


SectorWeights = SectorWeights/(sum(SectorWeights));
rad_shift =0.01;%0.015
slope = 9; levelshift = 2;
agridsize =50;%40
%%rpgridsize = 3500; %2000;
rpgridsize =450;%300
radgridsize =35;%25


if abs(sum(SectorWeights)-1)> 10^(-10), error('SectorWeights do not sum to one!'), end

% Maximum number of iterations on G
MaxItOnG = 60;

Ssize = agridsize*rpgridsize*radgridsize;

% Solve for the flexible price steady state 
%****************************************************************

par1 = sm*(theta-1)/(theta-sm*(theta-1));

FlexSSC = FlexSSL*par1^(sm/(1-sm))*(1+par1)^(-1/(1-sm));
FlexSSM = par1*FlexSSC;
FlexSSY = FlexSSC + FlexSSM;

omega = (theta-1)/theta*(1-sm)*(1+par1)*FlexSSL^(-psi-1)*FlexSSC^(1-gamma); % Level parameter on disutility of labor
omega2 = omega*(FlexSSL)^psi; % Marginal disutility of changing prices


K  = [param_agg(2)   mu_c ]'; 

K2 = K/4000;
K = K*FlexSSY;
K2 = K2*FlexSSY;

FlexSSY = log(FlexSSY);
FlexSSL = log(FlexSSL);
FlexSSC = log(FlexSSC);
if sm > 0
    FlexSSM = log(FlexSSM);
end

% Set gridsizes and grid max and min
%****************************************************************

MaxUncondVar = max(((sigma_eps.^2)./(1-rho.^2)).^(1/2));
MinUncondVar = min(((sigma_eps.^2)./(1-rho.^2)).^(1/2));
MinUncondVar = max(MinUncondVar,sigma_eta);

trunc_eps = 2.5;
amax = trunc_eps*MaxUncondVar;
amin = -trunc_eps*MaxUncondVar;
ainc = (amax-amin)/(agridsize-1) - mod((amax-amin)/(agridsize-1),10^(-5));
amin = amin - mod(amin,10^(-5));
amax = amin + (agridsize-1)*ainc;
ainc
fprintf('Gridpoints for "a" off of which the least volatile sector is simulated:\n')
fprintf('2*trunc_eps*MinUncondVar/ainc = %5.3f\n\n',...
    2*trunc_eps*MinUncondVar/ainc)
% if 2*trunc_eps*MinUncondVar/ainc < 20
%     error('2*trunc_eps*MinUncondVar/ainc < 20: Results unreliable!',...
%         2*trunc_eps*MinUncondVar/ainc) %#ok<CTPCT>
% end

% rp denotes the real price
% np denotes the nominal price
% The rp grid is a grid for the log of the real price
pimult = 250; % Determines sensitivity of pigrid to mu
rpmax = -amin*(1+pimult*abs(mu));
rpmin = -amax*(1+pimult*abs(mu));
if rpmax < 0.15
    rpmax = 0.15;
    rpmin = -0.15;
end
% %ajout ERwan 18 avril 2017
%  rpmax = 0.3;
%  rpmin = -0.3;

rpinc = (rpmax-rpmin)/(rpgridsize-1) - mod((rpmax-rpmin)/(rpgridsize-1),10^(-5));
rpmin = rpmin - mod(rpmin,10^(-5));
rpmax = rpmin + (rpgridsize-1)*rpinc;

% if rpinc > 0.0075
%     error('rpinc > 0.0075: Results unreliable')
% end

radmin = FlexSSC - radgridsize/2*rpinc + rad_shift;

% Create the real price and idiosyncratic productivity vectors
%**************************************************************

a = amin:ainc:amax; a = a';

rp = zeros(rpgridsize,1);
rp(1) = rpmin;
for ii = 2:rpgridsize
    rp(ii) = rp(ii-1) + rpinc;
end

rad = zeros(radgridsize,1);
rad(1) = radmin;
for ii = 2:radgridsize
    rad(ii) = rad(ii-1) + rpinc;
end

% Create Probability Distribution for the idiosyncratic shock
%**************************************************************
% Proba is a matrix that gives transition probabilities of going
% from state a to state a', i.e. Proba(i,j) = Prob(a' = j | a = i)
% 
% The procedure of Tauchen (1986) is used to approximate the 
% AR(1) process for log(A_it)

for ii = 1:NSectors
   % Proba(ii).Proba = CreateProba_KR(rho(ii),sigma_eps(ii),a, pa(ii));
    Proba(ii).Proba = CreateProba(rho(ii),sigma_eps(ii),a);
end

% Create probability distribution for nominal aggregate demand
%***************************************************************

ProbNgr = CreateProbNgr(mu,sigma_eta,rad);

% Guess a matrix G which gives the log inflation rate given S_t/P_t-1
%**************************************************************

G = zeros(radgridsize,1);
%G = (rp(2)-rp(1))*ones(radgridsize,1);
G(1,1) = -(radgridsize/(2*slope)-mod(radgridsize/(2*slope),1))*(rp(2)-rp(1)) ...
    + levelshift*(rp(2)-rp(1));
for ii = 2:radgridsize
    if mod(ii,slope) == 0
        G(ii,1) = G(ii-1,1) + rp(2) - rp(1);
    else
        G(ii,1) = G(ii-1,1);
    end
end

% Calculate the profit function
%**************************************************************

par1 = psi+1;
par2 = gamma;
par3 = exp(FlexSSC)/exp(FlexSSY);
par4 = exp(FlexSSM)/exp(FlexSSY) - sm;
par5 = 1-sm;

a3d = repmat(a,[1 rpgridsize radgridsize]);

rp3d = repmat(rp,[1 agridsize radgridsize]);
rp3d = permute(rp3d, [2 1 3]);

rad3d = repmat(rad,[1 agridsize rpgridsize]);
rad3d = permute(rad3d,[2 3 1]);

if sm > 0
    l3d = FlexSSL + (par3+par2*par4)/(par5-par1*par4)*(rad3d-FlexSSC);
    m3d = FlexSSM + par1*(l3d - FlexSSL) + par2*(rad3d-FlexSSC);
else
    l3d = FlexSSL + (rad3d-FlexSSC);
    m3d = 0*rad3d;
end

rPi3d = exp(rad3d + m3d).*exp(rp3d).^(1-theta) ...
    - (1-sm)^(sm-1)*sm^(-sm)*omega^(1-sm)*exp(l3d).^(psi*(1-sm)).*exp(rad3d).^(gamma*(1-sm)).*exp(-a3d).*exp(rad3d+m3d).*exp(rp3d).^(-theta);
rPi = reshape(rPi3d,[Ssize 1]);

for ii = 1:NSectors
    menucost(ii).menucost = reshape(omega2*K(ii)*exp(rad3d).^gamma,[Ssize 1]);
end

for ii = 1:NSectors
    menucost2(ii).menucost2 = reshape(omega2*K2(ii)*exp(rad3d).^gamma,[Ssize 1]);
end

clear a3d rp3d rad3d rPi3d l3d m3d

% Calculate the ratio of marginal utility
%**************************************************************
% The (i,j)th element of RMU is the ratio of marginal utility in 
% state j of period t+1 to the marginal utility in state i of
% period t.

RMU = ((1./exp(rad))*(exp(rad)')).^(-gamma);

% Initialize ErV matrix (Expected Value next period)
%**************************************************************

for ii = 1:NSectors
    rV(ii).rV = 1.5*ones(Ssize, 1)*max(0,mean(rPi)/(1-beta));
end

rPi3d = reshape(rPi,[agridsize rpgridsize radgridsize]);
tolV = 0.005*rPi3d(floor(agridsize/2),floor(rpgridsize/2),floor(radgridsize/2))/(1-beta);
clear rPi3d
%tolV = 0.03;

% Initialize stationary distribution Q
%**************************************************************

for ii = 1:NSectors
    Q(ii).Q = ones(Ssize,1)/Ssize;
end

tolQ = Q(1).Q(1)/10;

% Solve for the Equilibrium
%**************************************************************

[G,rV,F,F2,Q] = EqSolverGeNCalvoPlus(rPi,menucost,menucost2,RMU,alphaCalvo,...
    beta,theta,a,rp,rad,Proba,ProbNgr,rV,Q,G,SectorWeights,tolV,tolQ,MaxItOnG,0);

GError = CalcGErrorMultiSectorCalvoPlus(Q,F,F2,G,alphaCalvo,a,rp,rad,theta,...
    Proba,ProbNgr,SectorWeights);

PCStats = RigidityStatsMultiSectorCalvoPlus(Q,F,F2,alphaCalvo,...
    SectorWeights,a,rp,rad);



 f2=PCStats.freq(2);
   avfracup2=PCStats.fracup(2);
  med2=PCStats.wmed(2);
  q12=PCStats.w25(2);
  q32=PCStats.w75(2);
  interq2=PCStats.interq(2);
  kur2=PCStats.kur(2);
 m_model1=[f2;avfracup2;     med2;    interq2; kur2];
  m_model1

end
